Aramaic Bible inside Plain English A wise lady generates a house together with foolish lady destroys they along with her give

Modern-day English Type An effective woman’s family unit members try stored along with her of the the girl understanding, however it will be missing by the the girl foolishness.

Douay-Rheims Bible A smart lady buildeth the girl household: nevertheless stupid usually pull-down together with her give which also which is depending.

Around the globe Simple Variation All smart lady builds her domestic, but the stupid one to rips they down together very own hand.

New Changed Standard Type The brand new smart lady produces their home, although dumb rips they down with her individual hand.

New Cardiovascular system English Bible Most of the smart woman produces the woman home, nevertheless stupid you to rips they off together with her individual hand.

World English Bible Every smart woman creates their household, but the stupid you to definitely rips it down together own give

Ruth 4:eleven «We have been witnesses,» told you this new parents and all sorts of the folks at entrance. «Get the lord make the lady entering your residence such as for instance Rachel and you may Leah, just who with her gathered the house away from Israel. ous during the Bethlehem.

Proverbs A silly child is the calamity regarding their father: additionally the contentions of a spouse is a continual shedding.

Proverbs 21:nine,19 It’s a good idea to help you live when you look at the a large part of housetop, than simply that have a beneficial brawling girl during the a wide house…

Definition of a horizontal asymptote: The line y = y₀ is a «horizontal asymptote» of f(x) if and only if f(x) approaches y₀ as x approaches + or — .

Definition of a vertical asymptote: The line x = x₀ is a «vertical asymptote» of f(x) if and only if f(x) approaches + or — as x approaches x₀ from the left or from the right.

Definition of a slant asymptote: the line y = ax + b is a «slant asymptote» of f(x) if and only if lim _{(x—>+/- )} f(x) = ax + b.

Definition of a concave up curve: f(x) is «concave up» at x₀ if and only if is increasing at x₀

Definition of a concave down curve: f(x) is «concave down» at x₀ if and only if is decreasing at x₀

The second derivative test: If f

exists at x₀ and is positive, then is concave up at x₀. If f exists and is negative, then f(x) is concave down at x₀. If does not exist or is zero, then the test fails.

Definition of a local maxima: A function f(x) has a local maximum at x₀ if and only if there exists some interval I containing x₀ such that f(x₀) >= f(x) for all x in I.

The initial derivative test getting local extrema: In the event that f(x) was growing ( > 0) for everybody x in certain interval (an excellent, x

Definition of a local minima: A function f(x) has a local minimum at x₀ if and only if there exists some interval I containing x₀ such that f(x₀) <= f(x) for all x in I.

Occurrence regarding regional extrema: All local extrema are present at the crucial issues, although not every important circumstances exist at regional extrema.

₀] and f(x) is decreasing ( < 0) for all x in some interval [x₀, b), then f(x) has a local maximum at x₀. If f(x) is decreasing ( < 0) for all x in some interval (a, x₀] and f(x) is increasing ( > 0) for all x in some interval [x₀, b), then f(x) has a local minimum at x₀.

The second derivative test for local extrema: If = 0 and > 0, then f(x) has a local minimum at x₀. If = 0 and < 0, then f(x) has a local maximum at x₀.

Definition of absolute maxima: y₀ is the «absolute maximum» of f(x) on I if and only if y₀ >= f(x) for all x on I.

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Definition of absolute minima: y₀ is the «absolute minimum» of f(x) on I if and only if y₀ <= f(x) for all x on I.

The ultimate worth theorem: If the f(x) try proceeded inside the a closed interval I, then f(x) provides one sheer maximum and another sheer minimal during the We.

Density away from natural maxima: If the f(x) is actually carried on inside the a close interval I, then pure maximum from f(x) when you look at the I is the restriction property value f(x) toward the regional maxima and endpoints into the We.

Thickness out of sheer minima: In the event the f(x) try continuing within the a closed interval I, then pure minimum of f(x) from inside the I ‘s the lowest value of f(x) on the regional minima and you will endpoints toward I.

Solution type of looking extrema: If f(x) are persisted into the a close period I, then natural extrema from f(x) inside the We can be found at important affairs and you may/or at the endpoints off We. (This is certainly a smaller particular brand of these.)